Question

Verify if x+y+z=0, show that x³ + y³ + z³ = 3xyz.​

Answer 1

Answer:

x+y=-z ->1

x³+y³+3xy(x+y)=-z³{cubing on both sides of the equation}

x³+y³+3xy(-z)=-z³{x+y=-z from 1 }

x³+y³+z³=3xyz

Answer 2

Answer:

In order to prove this ,

Let us use the formula :

x3 + y3 + z3 - 3xyz = ( x + y + z) (x2 + y2 + z2 - xy - yz - xz)

Now let us keep x + y + z = 0

So,

x3 + y3 + z3 - 3xyz = 0

x3 + y3 + z3 = 3xyz

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